Following [1]}, the Bayesian and generalized Bayesian frameworks can be considered simply as rules for using data to update prior beliefs to posterior beliefs. As such, it makes sense to consider how much information has been gained from the update, by comparing the prior to the posterior. Of course, this information gain depends on both the updating rule and on the data, and [2]} proposed a procedure for selecting the learning rate \(\eta \)  based on matching the expected information gain between Bayes and generalized Bayes updates.
